Finite Group Databasebeta

← #30620503

Subgroups — #30620503

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#446C211yesmaximal, characteristic, complemented
2#21462338C211yesmaximal, characteristic, complemented
3#21461987C211yesmaximal, characteristic
4#21461987C211yesmaximal, characteristic
5#21461985C211yesmaximal, characteristic, complemented
6#21461950C211yesmaximal, characteristic, complemented
7#21461949C211yesmaximal, characteristic
8#21461948C211yesmaximal, characteristic
9#21461690C211yesmaximal, characteristic, complemented
10#21461689C211yesmaximal, characteristic
11#21461688C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic
14C4×#14519840C211yesmaximal, characteristic, complemented
15#556×D61C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840812—21no—
20D61⋊(C4⋊C8)C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22D61⋊(C4⋊C8)C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519839C2211yescharacteristic
33C2×#14519839C2211yescharacteristic
34C2×#14519839C2211yescharacteristic
35#16840721C2211yescharacteristic
36#16840721C2211yescharacteristic
37C4×D61⋊C8C2211yescharacteristic
38(C2×#6923)⋊Q8—21no—
39#16840711—21no—
40#16840711—21no—
41#16840708C2211yescharacteristic
42#16840706C2211yescharacteristic
43#16840706C2211yescharacteristic
44C4⋊C4×#6923—21no—
45C4×C4⋊#6923C2211yescharacteristic
46C4×C4⋊#6923C2211yescharacteristic
47C4×C4⋊#6923C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840486C411yescharacteristic, complemented
53#16840485C411yescharacteristic, complemented
54#16840484C411yescharacteristic, complemented
55#16840484C411yescharacteristic, complemented
56#16840483—21no—
57#16840482C411yescharacteristic, complemented
58#16840481C411yescharacteristic, complemented
59#16840481C411yescharacteristic, complemented
60#16840480—21no—
61#16840479—21no—
62#16840479—21no—
63C4⋊Q8×D61C2211yescharacteristic
64#126×D61—21no—
65#126×D61—21no—
66#124×D61C2211yescharacteristic
67#124×D61C2211yescharacteristic
68C22⋊Q8×D61—21no—
69C4×Q8×D61C2211yescharacteristic
70C4×Q8×D61C2211yescharacteristic
71C4×Q8×D61C2211yescharacteristic
72C4×D4×D61C2211yescharacteristic
73#117×D61—21no—
74C61×#556C411yescharacteristic, complemented
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94#14519840—22no—
95#14519840—22no—
96#14519840—22no—
97#14519840—22no—
98#14519840—41no—
99#14519840—41no—
100#14519840—41no—
101#14519840—41no—
102#14519839—22no—
103#14519839—22no—
104#14519839—41no—
105#14519839—41no—
106#14519832—21no—
107#14519832—21no—
108#14519832—21no—
109#14519832—21no—
110C4×#92420—21no—
111C4×#92420—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×Q8×D61D411yescharacteristic
120C2×Q8×D61C2311yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×D4×D61C2311yescharacteristic
123C22×C4×D61—21no—
124#14519777C2×C411yescharacteristic
125#14519776—21no—
126#14519776—21no—
127#14519775C2×C411yescharacteristic
128#14519775C2×C411yescharacteristic
129#14519772—21no—
130#14519772—21no—
131#14519772—21no—
132#14519772—21no—
133#14519772—21no—
134#14519772—21no—
135#14519771—21no—
136#14519771—21no—
137#14519770—21no—
138#14519770—21no—
139#14519770—21no—
140#14519770—21no—
141#14519770—21no—
142#14519770—21no—
143#14519766C2×C411yescharacteristic
144#14519766C2×C411yescharacteristic
145#14519765C2×C411yescharacteristic
146#14519765C2×C411yescharacteristic
147#14519764C2×C411yescharacteristic
148#14519764C2×C411yescharacteristic
149#14519763—21no—
150#14519763—21no—
151#14519763—21no—
152#14519763—21no—
153#14519757—21no—
154#14519756—21no—
155#14519755—21no—
156#14519755—21no—
157#14519754—21no—
158#14519754—21no—
159#14519753—21no—
160Q8×Dic61C2×C411yescharacteristic
161Q8×Dic61C2×C411yescharacteristic
162Q8×Dic61D411yescharacteristic
163C4×Dic122—21no—
164C4×Dic122—21no—
165C4×Dic122C2×C411yescharacteristic
166C4×Dic122C2×C411yescharacteristic
167C4×Dic122C2×C411yescharacteristic
168C4×Dic122C2×C411yescharacteristic
169C4×Dic122C2×C411yescharacteristic
170#14519742—21no—
171#14519742—21no—
172#14519742C2×C411yescharacteristic
173#14519742C2×C411yescharacteristic
174#14519742D411yescharacteristic
175#14519742D411yescharacteristic
176#14519742D411yescharacteristic
177C4×D244C2×C411yescharacteristic
178D4×Dic61C2×C411yescharacteristic
179#14519739C2×C411yescharacteristic
180C4×C22⋊D61—21no—
181#14519737—21no—
182#14519736—21no—
183#14519735—21no—
184#14519735—21no—
185#14519734—21no—
186#14519734—21no—
187#14519733—21no—
188#14519733—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61D411yescharacteristic
194C4⋊C4×D61D411yescharacteristic
195C4⋊C4×D61D411yescharacteristic
196C4⋊C4×D61C2311yescharacteristic
197C22⋊C4×D61—21no—
198C22⋊C4×D61—21no—
199C22⋊C4×D61—21no—
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C42×D61—21no—
203C42×D61—21no—
204C42×D61C2311yescharacteristic
205C42×D61C2311yescharacteristic
206C42×D61C2311yescharacteristic
207C4⋊Q8×C61C2×C411yescharacteristic
208#126×C61—21no—
209#126×C61—21no—
210#124×C61C2×C411yescharacteristic
211#124×C61C2×C411yescharacteristic
212C22⋊Q8×C61—21no—
213C4×Q8×C61C2×C411yescharacteristic
214C4×Q8×C61C2×C411yescharacteristic
215C4×Q8×C61C2×C411yescharacteristic
216C4×D4×C61C2×C411yescharacteristic
217#117×C61—21no—
218C23×D61—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C2×Q8×C61C22⋊C411yescharacteristic
224C2×Q8×C61C22×C411yescharacteristic
225C2×Q8×C61C22×C411yescharacteristic
226C2×D4×C61C22×C411yescharacteristic
227C22×C4×C61—21no—
228C2×C22⋊D61—21no—
229C22×Dic61—21no—
230Q8×D61—21no—
231Q8×D61—21no—
232Q8×D61—21no—
233Q8×D61—21no—
234Q8×D61—21no—
235Q8×D61—21no—
236Q8×D61—21no—
237Q8×D61—21no—
238Q8×D61—41no—
239Q8×D61—41no—
240D4×D61—21no—
241D4×D61—21no—
242D4×D61—21no—
243D4×D61—21no—
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122—21no—
261C2×Dic122C22⋊C411yescharacteristic
262C2×Dic122C22⋊C411yescharacteristic
263C2×Dic122C22⋊C411yescharacteristic
264C2×Dic122C22×C411yescharacteristic
265C2×Dic122C22×C411yescharacteristic
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—21no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—21no—
276C4⋊#6923—21no—
277C4⋊#6923—42no—
278C4⋊#6923—81no—
279C4⋊#6923#4112yes—
280C4×#6923—42no—
281C4×#6923—81no—
282C4×#6923—81no—
283D61⋊C8—21no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8—21no—
287D61⋊C8—21no—
288D61⋊C8—21no—
289D61⋊C8—21no—
290D61⋊C8#4112yes—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61C22⋊C411yescharacteristic
296C4⋊C4×C61C22⋊C411yescharacteristic
297C4⋊C4×C61C22⋊C411yescharacteristic
298C4⋊C4×C61C22×C411yescharacteristic
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C42×C61—21no—
305C42×C61—21no—
306C42×C61C22×C411yescharacteristic
307C42×C61C22×C411yescharacteristic
308C42×C61C22×C411yescharacteristic
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61—21no—
328C4⋊Dic61C22⋊C411yescharacteristic
329C4⋊Dic61C22⋊C411yescharacteristic
330C4⋊Dic61C22⋊C411yescharacteristic
331C4⋊Dic61C22×C411yescharacteristic
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343#11758196C22⋊C411yescharacteristic
344#11758196C22⋊C411yescharacteristic
345#11758196C22⋊C411yescharacteristic
346#11758196C22⋊C411yescharacteristic
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61C22×C411yescharacteristic
354C4×Dic61C22×C411yescharacteristic
355C4×Dic61C22×C411yescharacteristic
356C4×Dic61C2×D411yescharacteristic
357C4×Dic61C2×D411yescharacteristic
358C4×Dic61C2×D411yescharacteristic
359C4×Dic61C2×D411yescharacteristic
360C4×Dic61C2×D411yescharacteristic
361C4×Dic61C2×D411yescharacteristic
362C23×C61—21no—
363C22×D61—21no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61C22×D411yescharacteristic
371C2×#6923—22no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—41no—
376C2×#6923—41no—
377C2×#6923—41no—
378C2×#6923—41no—
379C2×#6923—41no—
380C2×#6923—41no—
381C2×#6923—41no—
382C2×#6923—41no—
383Q8×C61—21no—
384Q8×C61—21no—
385Q8×C61—21no—
386Q8×C61—21no—
387Q8×C61—41no—
388D4×C61—21no—
389D4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—42no—
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C2×C4×C61C2×C22⋊C411yescharacteristic
399C2×C4×C61C2×C22⋊C411yescharacteristic
400C2×C4×C61C23×C411yescharacteristic
401C22⋊D61—41no—
402C22⋊D61—41no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—42no—
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C22×D411yescharacteristic
414D244—21no—
415D244—21no—
416C4×D61—21no—
417C4×D61—21no—
418C4×D61—21no—
419C4×D61—21no—
420C4×D61—21no—
421C4×D61—21no—
422C4×D61—21no—
423C4×D61—21no—
424C4×D61—21no—
425C4×D61—21no—
426C4×D61—21no—
427C4×D61—21no—
428C4×D61—42no—
429C4×D61—42no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61C2×#4111yescharacteristic
437C4×D61C2×#4111yescharacteristic
438C4×D61H(5,𝔽2)11yescharacteristic
439C4×D612−1+411yescharacteristic
440Dic122—21no—
441Dic122—21no—
442Dic122—21no—
443Dic122—21no—
444Dic122—41no—
445Dic122—41no—
446Dic122—41no—
447Dic122—41no—
448Dic122—41no—
449Dic122—41no—
450Dic122—41no—
451#92420—22no—
452#92420—41no—
453#92420—41no—
454#92420—41no—
455#22548—611nomaximal, Sylow
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61C22×C22⋊C411yescharacteristic
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—81no—
464C2×D61—81no—
465C2×D61—81no—
466C2×D61—81no—
467C2×D61#54811yescharacteristic
468C2×D61#55011yescharacteristic
469C2×D61#57511yescharacteristic
470C2×D61#57511yescharacteristic
471C2×D61#57711yescharacteristic
472C2×D61#57811yescharacteristic
473#6923—42no—
474#6923—81no—
475#6923—81no—
476#6923—81no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—41no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61C4×#4111yescharacteristic
487C4×C61#52011yescharacteristic
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—21no—
493Dic61—21no—
494Dic61—41no—
495Dic61—41no—
496Dic61—41no—
497Dic61#54811yescharacteristic
498Dic61#55011yescharacteristic
499C2×#556—611no—
500C2×#446—611no—
501#2355—611no—
502#1983—611no—
503#1983—611no—
504#1981—611no—
505#1960—611no—
506#1959—611no—
507#1958—611no—
508#1805—611no—
509#1804—611no—
510#1803—611no—
511#1763—611no—
512#1762—611no—
513C4×#103—611no—
514C2×C61—81no—
515C2×C61#234111yescharacteristic
516C2×C61#289611yescharacteristic
517C2×C61#289811yescharacteristic
518D61—81no—
519D61#337611yescharacteristic
520D61#337711yescharacteristic
521D61#340111yescharacteristic
522D61#340211yescharacteristic
523#556—611no—
524#556—611no—
525#556—611no—
526#556—611no—
527#556—611no—
528#556—611no—
529#556—611no—
530#556—1221no—
531#556—1221no—
532#556—1221no—
533#556—1221no—
534#556#692311yescharacteristic, complemented
535C2×C4⋊Q8—611no—
536C2×#126—1221no—
537C2×#126—1221no—
538C2×#124—611no—
539C2×#124—611no—
540C2×C22⋊Q8—1221no—
541C2×C4×Q8—611no—
542C2×C4×Q8—611no—
543C2×C4×Q8—611no—
544C2×C4×D4—611no—
545C2×#117—1221no—
546#446—1221no—
547#446—1221no—
548#446—1221no—
549#446—1221no—
550C2×C4⋊C8—611no—
551C2×C4⋊C8—611no—
552C2×C4⋊C8—611no—
553C2×#103—611no—
554C2×#103—611no—
555C2×#103—611no—
556C2×#103—611no—
557C2×#103—611no—
558C2×#103—611no—
559C2×#103—611no—
560C2×#103—611no—
561C2×#102—611no—
562C2×#102—611no—
563C2×#102—611no—
564C2×#102—611no—
565C2×#97—611no—
566C2×#97—611no—
567C2×C4×C8—611no—
568#391—1221no—
569#387—1221no—
570#387—1221no—
571#384—611no—
572#382—611no—
573#382—611no—
574C4×C4⋊C4—611no—
575C4×C4⋊C4—611no—
576C4×C4⋊C4—611no—
577C4×C4⋊C4—1221no—
578#340—611no—
579#340—611no—
580#340—611no—
581#340—611no—
582C61#2254811yescharacteristic, complemented, Sylow
583C22×Q8—611no—
584C22×Q8—611no—
585C22×Q8—611no—
586C22×D4—611no—
587C23×C4—1221no—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8—611no—
591C22×C8—611no—
592C4⋊Q8—611no—
593C4⋊Q8—611no—
594C4⋊Q8—611no—
595C4⋊Q8—1221no—
596C4⋊Q8—1221no—
597C4⋊Q8C2×#692311yescharacteristic
598#126—21no—
599#126—21no—
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#126—1221no—
604#126—1221no—
605#126—1221no—
606#126—1221no—
607#126—1221no—
608#126—1221no—
609#126—1221no—
610#126—1221no—
611#126—1221no—
612#126—1221no—
613#126—1221no—
614#124—611no—
615#124—611no—
616#124—611no—
617#124—611no—
618#124—611no—
619#124—611no—
620#124—1221no—
621#124—1221no—
622#124—1221no—
623#124—1221no—
624#124C2×#692311yescharacteristic
625#124C2×#692311yescharacteristic
626C22⋊Q8—21no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8—1221no—
633C22⋊Q8—1221no—
634C4×Q8—611no—
635C4×Q8—611no—
636C4×Q8—611no—
637C4×Q8—611no—
638C4×Q8—611no—
639C4×Q8—611no—
640C4×Q8—611no—
641C4×Q8—611no—
642C4×Q8—611no—
643C4×Q8—611no—
644C4×Q8—611no—
645C4×Q8—611no—
646C4×Q8—611no—
647C4×Q8—1221no—
648C4×Q8—1221no—
649C4×Q8—1221no—
650C4×Q8—1221no—
651C4×Q8C2×#692311yescharacteristic
652C4×Q8C2×#692311yescharacteristic
653C4×Q8C2×#692311yescharacteristic
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4C2×#692311yescharacteristic
660#117—21no—
661#117—1221no—
662#117—1221no—
663#117—1221no—
664#117—1221no—
665#117—1221no—
666#117—1221no—
667#117—1221no—
668C2×C4⋊C4—611no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—611no—
671C2×C4⋊C4—611no—
672C2×C4⋊C4—611no—
673C2×C4⋊C4—611no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C4⋊C4—1221no—
681C2×C4⋊C4—1221no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C42—611no—
688C2×C42—611no—
689C2×C42—611no—
690C2×C42—1221no—
691C2×C42—1221no—
692C2×C42—1221no—
693C2×C42—1221no—
694C2×C42—1221no—
695C4⋊C8—1221no—
696C4⋊C8—1221no—
697C4⋊C8—1221no—
698C4⋊C8—1221no—
699C4⋊C8—1221no—
700C4⋊C8—1221no—
701#103—1222no—
702#103—1222no—
703#103—1222no—
704#103—1222no—
705#103—2441no—
706#103—2441no—
707#103—2441no—
708#103—2441no—
709#102—1222no—
710#102—1222no—
711#102—2441no—
712#102—2441no—
713#97—1221no—
714#97—1221no—
715#97—1221no—
716#97—1221no—
717C4×C8—1221no—
718C4×C8—1221no—
719#95—1221no—
720#95—1221no—
721#95—1221no—
722#95—1221no—
723#95—1221no—
724#95—1221no—
725#95—1221no—
726C24—1221no—
727C2×Q8—611no—
728C2×Q8—611no—
729C2×Q8—611no—
730C2×Q8—611no—
731C2×Q8—611no—
732C2×Q8—1221no—
733C2×Q8—1221no—
734C2×Q8—1221no—
735C2×Q8—1221no—
736C2×Q8—1221no—
737C2×Q8—1221no—
738C2×Q8—1221no—
739C2×Q8—1221no—
740C2×Q8—1221no—
741C2×Q8—1221no—
742C2×Q8—2441no—
743C2×Q8—2441no—
744C2×Q8C22⋊#692311yescharacteristic
745C2×Q8C22×#692311yescharacteristic
746C2×Q8C22×#692311yescharacteristic
747C2×D4—611no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4C22×#692311yescharacteristic
754C22×C4—21no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—2442no—
773C22×C4—2442no—
774C2×C8—612no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—611no—
798C4⋊C4—611no—
799C4⋊C4—612no—
800C4⋊C4—611no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4—1221no—
819C4⋊C4—1221no—
820C4⋊C4—1221no—
821C4⋊C4—4881no—
822C4⋊C4—2442no—
823C4⋊C4C22⋊#692311yescharacteristic
824C4⋊C4C22⋊#692311yescharacteristic
825C4⋊C4C22⋊#692311yescharacteristic
826C4⋊C4C22×#692311yescharacteristic
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4—1221no—
845C22⋊C4—1221no—
846C22⋊C4—1221no—
847C42—21no—
848C42—21no—
849C42—611no—
850C42—611no—
851C42—611no—
852C42—611no—
853C42—611no—
854C42—611no—
855C42—611no—
856C42—611no—
857C42—611no—
858C42—1221no—
859C42—1221no—
860C42—1221no—
861C42—1221no—
862C42—1221no—
863C42—1221no—
864C42—4881no—
865C42—4881no—
866C42—2442no—
867C42C22×#692311yescharacteristic
868C42C22×#692311yescharacteristic
869C42C22×#692311yescharacteristic
870C23—21no—
871C23—611no—
872C23—1221no—
873C23—2441no—
874C23—2441no—
875C23—2441no—
876C23—2441no—
877C23—2441no—
878C23—2441no—
879Q8—21no—
880Q8—21no—
881Q8—21no—
882Q8—21no—
883Q8—41no—
884Q8—1221no—
885Q8—1221no—
886Q8—1221no—
887Q8—1221no—
888Q8—2441no—
889Q8—2441no—
890Q8—2441no—
891Q8—2441no—
892Q8—2441no—
893Q8—2441no—
894Q8—2441no—
895D4—21no—
896D4—21no—
897D4—1221no—
898D4—1221no—
899D4—2441no—
900D4—2441no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—42no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—1221no—
928C2×C4—1222no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—1221no—
932C2×C4—2442no—
933C2×C4—2442no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2442no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4C2×C22⋊#692311yescharacteristic
953C2×C4C2×C22⋊#692311yescharacteristic
954C2×C4C2×C22⋊#692311yescharacteristic
955C2×C4C2×C22⋊#692311yescharacteristic
956C2×C4C2×C22⋊#692311yescharacteristic
957C2×C4C2×C22⋊#692311yescharacteristic
958C2×C4C23×#692311yescharacteristic
959C8—1222no—
960C8—2441no—
961C8—2441no—
962C8—2441no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22—611no—
970C22—611no—
971C22—611no—
972C22—4881no—
973C22—4881no—
974C22—4881no—
975C22—4881no—
976C22—2441no—
977C22—2441no—
978C22—2441no—
979C22C22×C22⋊#692311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—611no—
990C4—611no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—1221no—
995C4—1221no—
996C4—1221no—
997C4—4881no—
998C4—4881no—
999C4—4881no—
1000C4—2442no—
1001C4—2441no—
1002C4—2441no—
1003C4—2441no—
1004C4#41×#692311yescharacteristic
1005C4#1684083111yescharacteristic
1006C2—81no—
1007C2—611no—
1008C2—611no—
1009C2—611no—
1010C2—611no—
1011C2—4881no—
1012C2#2146232411yescharacteristic
1013C2#2146243911yescharacteristic
1014C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#556C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#556#6923
hypocenterC61#22548
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D61⋊#446C2semidirect
2. #21462338C2semidirect
5. #21461985C2semidirect
6. #21461950C2semidirect
9. #21461690C2semidirect
11. #21461688C2semidirect
12. #21461591C2semidirect
14. C4×#14519840C2semidirect
52. #16840486C4semidirect
53. #16840485C4semidirect
54. #16840484C4semidirect
55. #16840484C4semidirect
57. #16840482C4semidirect
58. #16840481C4semidirect
59. #16840481C4semidirect
74. C61×#556C4semidirect
534. #556#6923semidirect
582. C61#22548semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D61⋊#4462
#214623382
#214619872
#214619852
#214619502
#214619492
#214619482
#214616902
#214616892
#214616882
#214615912
#214615892
C4×#145198402
#556×D612
#2254861